Abstract
A Dirichlet region for an optimal mass transportation problem is, roughly speaking, a zone in which the transportation cost is vanishing. We study the optimal transportation problem with an unknown Dirichlet region Σ which varies in the class of closed connected subsets having prescribed 1-dimensional Hausdorff measure. We show the existence of an optimal Σ opt and study some of its geometrical properties. We also present numerical computations which show the shape of Σ opt in some model examples.KeywordsSingular PointTransportation ProblemTransport PlanLength ConstraintHausdorff ConvergenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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